Team 1034 Page 10 of 21 Figure 3: Illustration of creating divisions by first subdividing the map. Left: Population density distribution of hypothetical map with five desired districts. Middle: A subdivision of the map into two regions generated from two unshown generator points. Right: Final division of each subregion from the middle figure into desired final divisions degeneracy of generator pt. =m As we will see when we apply our model to New York, this method works well. It should be noted, though, that this is not the only way to define the location of generator points, but it is a very good start 4.4 Procedure for Creating Regions using Voronoi and Voronoiesque Diagrams Once we have our generator points, we can generate our diagrams with two more steps first generate the diagram using the given generator points. Within each generated region called a subdivision, with some degeneracy r, create r new generator points within that subdivision by finding the r largest population density peaks and create another diagram ee fig 3 5 Redistricting in New York State At this point, we have described a general procedure for generating political districts with Voronoi diagrams which seems effective. We now turn our attention to testing our models on New York has regions with large population density, has regions with constrained geography, and must be divided into many(29) regionsTeam 1034 Page 10 of 21 Figure 3: Illustration of creating divisions by first subdividing the map. Left: Population density distribution of hypothetical map with five desired districts. Middle: A subdivision of the map into two regions generated from two unshown generator points. Right: Final division of each subregion from the middle figure into desired final divisions. X all generator pts. degeneracy of generator pt. = m As we will see when we apply our model to New York, this method works well. It should be noted, though, that this is not the only way to define the location of generator points, but it is a very good start. 4.4 Procedure for Creating Regions using Voronoi and Voronoiesque Diagrams Once we have our generator points, we can generate our diagrams with two more steps: first generate the diagram using the given generator points. Within each generated region, called a subdivision, with some degeneracy r, create r new generator points within that subdivision by finding the r largest population density peaks and create another diagram. See fig.3 5 Redistricting in New York State At this point, we have described a general procedure for generating political districts with Voronoi diagrams which seems effective. We now turn our attention to testing our models on New York. • has regions with large population density, • has regions with constrained geography, • and must be divided into many (29) regions